Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4009,2,Mod(1,4009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4009, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4009.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4009 = 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4009.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0120261703\) |
Analytic rank: | \(1\) |
Dimension: | \(71\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.31 | ||
Character | \(\chi\) | \(=\) | 4009.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.893036 | −0.631472 | −0.315736 | − | 0.948847i | \(-0.602251\pi\) | ||||
−0.315736 | + | 0.948847i | \(0.602251\pi\) | |||||||
\(3\) | −2.08830 | −1.20568 | −0.602839 | − | 0.797863i | \(-0.705964\pi\) | ||||
−0.602839 | + | 0.797863i | \(0.705964\pi\) | |||||||
\(4\) | −1.20249 | −0.601243 | ||||||||
\(5\) | −3.63561 | −1.62589 | −0.812947 | − | 0.582337i | \(-0.802138\pi\) | ||||
−0.812947 | + | 0.582337i | \(0.802138\pi\) | |||||||
\(6\) | 1.86492 | 0.761352 | ||||||||
\(7\) | −2.58906 | −0.978572 | −0.489286 | − | 0.872123i | \(-0.662743\pi\) | ||||
−0.489286 | + | 0.872123i | \(0.662743\pi\) | |||||||
\(8\) | 2.85994 | 1.01114 | ||||||||
\(9\) | 1.36098 | 0.453659 | ||||||||
\(10\) | 3.24673 | 1.02671 | ||||||||
\(11\) | −1.15709 | −0.348875 | −0.174437 | − | 0.984668i | \(-0.555811\pi\) | ||||
−0.174437 | + | 0.984668i | \(0.555811\pi\) | |||||||
\(12\) | 2.51115 | 0.724906 | ||||||||
\(13\) | −5.25839 | −1.45841 | −0.729207 | − | 0.684293i | \(-0.760111\pi\) | ||||
−0.729207 | + | 0.684293i | \(0.760111\pi\) | |||||||
\(14\) | 2.31212 | 0.617941 | ||||||||
\(15\) | 7.59223 | 1.96031 | ||||||||
\(16\) | −0.149054 | −0.0372635 | ||||||||
\(17\) | −4.71801 | −1.14428 | −0.572142 | − | 0.820154i | \(-0.693887\pi\) | ||||
−0.572142 | + | 0.820154i | \(0.693887\pi\) | |||||||
\(18\) | −1.21540 | −0.286473 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 4.37177 | 0.977558 | ||||||||
\(21\) | 5.40672 | 1.17984 | ||||||||
\(22\) | 1.03332 | 0.220305 | ||||||||
\(23\) | −5.80291 | −1.20999 | −0.604996 | − | 0.796229i | \(-0.706825\pi\) | ||||
−0.604996 | + | 0.796229i | \(0.706825\pi\) | |||||||
\(24\) | −5.97239 | −1.21911 | ||||||||
\(25\) | 8.21767 | 1.64353 | ||||||||
\(26\) | 4.69593 | 0.920948 | ||||||||
\(27\) | 3.42276 | 0.658711 | ||||||||
\(28\) | 3.11331 | 0.588360 | ||||||||
\(29\) | −9.27186 | −1.72174 | −0.860871 | − | 0.508823i | \(-0.830081\pi\) | ||||
−0.860871 | + | 0.508823i | \(0.830081\pi\) | |||||||
\(30\) | −6.78014 | −1.23788 | ||||||||
\(31\) | −1.62332 | −0.291556 | −0.145778 | − | 0.989317i | \(-0.546569\pi\) | ||||
−0.145778 | + | 0.989317i | \(0.546569\pi\) | |||||||
\(32\) | −5.58676 | −0.987609 | ||||||||
\(33\) | 2.41634 | 0.420631 | ||||||||
\(34\) | 4.21335 | 0.722584 | ||||||||
\(35\) | 9.41281 | 1.59106 | ||||||||
\(36\) | −1.63656 | −0.272759 | ||||||||
\(37\) | 2.08729 | 0.343148 | 0.171574 | − | 0.985171i | \(-0.445115\pi\) | ||||
0.171574 | + | 0.985171i | \(0.445115\pi\) | |||||||
\(38\) | −0.893036 | −0.144870 | ||||||||
\(39\) | 10.9811 | 1.75838 | ||||||||
\(40\) | −10.3976 | −1.64401 | ||||||||
\(41\) | 3.49915 | 0.546475 | 0.273238 | − | 0.961947i | \(-0.411905\pi\) | ||||
0.273238 | + | 0.961947i | \(0.411905\pi\) | |||||||
\(42\) | −4.82840 | −0.745038 | ||||||||
\(43\) | 7.33492 | 1.11856 | 0.559282 | − | 0.828977i | \(-0.311077\pi\) | ||||
0.559282 | + | 0.828977i | \(0.311077\pi\) | |||||||
\(44\) | 1.39138 | 0.209759 | ||||||||
\(45\) | −4.94798 | −0.737602 | ||||||||
\(46\) | 5.18221 | 0.764075 | ||||||||
\(47\) | 5.98392 | 0.872844 | 0.436422 | − | 0.899742i | \(-0.356246\pi\) | ||||
0.436422 | + | 0.899742i | \(0.356246\pi\) | |||||||
\(48\) | 0.311269 | 0.0449278 | ||||||||
\(49\) | −0.296775 | −0.0423964 | ||||||||
\(50\) | −7.33867 | −1.03785 | ||||||||
\(51\) | 9.85259 | 1.37964 | ||||||||
\(52\) | 6.32314 | 0.876862 | ||||||||
\(53\) | 5.97254 | 0.820392 | 0.410196 | − | 0.911997i | \(-0.365460\pi\) | ||||
0.410196 | + | 0.911997i | \(0.365460\pi\) | |||||||
\(54\) | −3.05665 | −0.415958 | ||||||||
\(55\) | 4.20672 | 0.567234 | ||||||||
\(56\) | −7.40454 | −0.989474 | ||||||||
\(57\) | −2.08830 | −0.276601 | ||||||||
\(58\) | 8.28011 | 1.08723 | ||||||||
\(59\) | 9.14132 | 1.19010 | 0.595049 | − | 0.803689i | \(-0.297132\pi\) | ||||
0.595049 | + | 0.803689i | \(0.297132\pi\) | |||||||
\(60\) | −9.12955 | −1.17862 | ||||||||
\(61\) | −5.99586 | −0.767692 | −0.383846 | − | 0.923397i | \(-0.625401\pi\) | ||||
−0.383846 | + | 0.923397i | \(0.625401\pi\) | |||||||
\(62\) | 1.44968 | 0.184110 | ||||||||
\(63\) | −3.52365 | −0.443938 | ||||||||
\(64\) | 5.28729 | 0.660911 | ||||||||
\(65\) | 19.1175 | 2.37123 | ||||||||
\(66\) | −2.15788 | −0.265616 | ||||||||
\(67\) | 3.69923 | 0.451933 | 0.225966 | − | 0.974135i | \(-0.427446\pi\) | ||||
0.225966 | + | 0.974135i | \(0.427446\pi\) | |||||||
\(68\) | 5.67334 | 0.687993 | ||||||||
\(69\) | 12.1182 | 1.45886 | ||||||||
\(70\) | −8.40598 | −1.00471 | ||||||||
\(71\) | −1.78491 | −0.211830 | −0.105915 | − | 0.994375i | \(-0.533777\pi\) | ||||
−0.105915 | + | 0.994375i | \(0.533777\pi\) | |||||||
\(72\) | 3.89231 | 0.458713 | ||||||||
\(73\) | −5.50261 | −0.644032 | −0.322016 | − | 0.946734i | \(-0.604360\pi\) | ||||
−0.322016 | + | 0.946734i | \(0.604360\pi\) | |||||||
\(74\) | −1.86402 | −0.216688 | ||||||||
\(75\) | −17.1609 | −1.98157 | ||||||||
\(76\) | −1.20249 | −0.137935 | ||||||||
\(77\) | 2.99577 | 0.341399 | ||||||||
\(78\) | −9.80649 | −1.11037 | ||||||||
\(79\) | 4.42549 | 0.497907 | 0.248953 | − | 0.968515i | \(-0.419913\pi\) | ||||
0.248953 | + | 0.968515i | \(0.419913\pi\) | |||||||
\(80\) | 0.541902 | 0.0605865 | ||||||||
\(81\) | −11.2307 | −1.24785 | ||||||||
\(82\) | −3.12487 | −0.345084 | ||||||||
\(83\) | 14.7807 | 1.62240 | 0.811199 | − | 0.584770i | \(-0.198815\pi\) | ||||
0.811199 | + | 0.584770i | \(0.198815\pi\) | |||||||
\(84\) | −6.50151 | −0.709372 | ||||||||
\(85\) | 17.1528 | 1.86049 | ||||||||
\(86\) | −6.55035 | −0.706342 | ||||||||
\(87\) | 19.3624 | 2.07587 | ||||||||
\(88\) | −3.30919 | −0.352761 | ||||||||
\(89\) | 1.50034 | 0.159036 | 0.0795178 | − | 0.996833i | \(-0.474662\pi\) | ||||
0.0795178 | + | 0.996833i | \(0.474662\pi\) | |||||||
\(90\) | 4.41873 | 0.465775 | ||||||||
\(91\) | 13.6143 | 1.42716 | ||||||||
\(92\) | 6.97792 | 0.727499 | ||||||||
\(93\) | 3.38996 | 0.351523 | ||||||||
\(94\) | −5.34385 | −0.551176 | ||||||||
\(95\) | −3.63561 | −0.373006 | ||||||||
\(96\) | 11.6668 | 1.19074 | ||||||||
\(97\) | 10.2071 | 1.03638 | 0.518188 | − | 0.855267i | \(-0.326607\pi\) | ||||
0.518188 | + | 0.855267i | \(0.326607\pi\) | |||||||
\(98\) | 0.265031 | 0.0267722 | ||||||||
\(99\) | −1.57477 | −0.158270 | ||||||||
\(100\) | −9.88163 | −0.988163 | ||||||||
\(101\) | −9.67000 | −0.962201 | −0.481101 | − | 0.876665i | \(-0.659763\pi\) | ||||
−0.481101 | + | 0.876665i | \(0.659763\pi\) | |||||||
\(102\) | −8.79872 | −0.871203 | ||||||||
\(103\) | 14.8149 | 1.45976 | 0.729879 | − | 0.683576i | \(-0.239576\pi\) | ||||
0.729879 | + | 0.683576i | \(0.239576\pi\) | |||||||
\(104\) | −15.0387 | −1.47466 | ||||||||
\(105\) | −19.6567 | −1.91830 | ||||||||
\(106\) | −5.33370 | −0.518054 | ||||||||
\(107\) | −13.5153 | −1.30657 | −0.653285 | − | 0.757112i | \(-0.726610\pi\) | ||||
−0.653285 | + | 0.757112i | \(0.726610\pi\) | |||||||
\(108\) | −4.11583 | −0.396046 | ||||||||
\(109\) | 12.1046 | 1.15941 | 0.579704 | − | 0.814827i | \(-0.303168\pi\) | ||||
0.579704 | + | 0.814827i | \(0.303168\pi\) | |||||||
\(110\) | −3.75675 | −0.358192 | ||||||||
\(111\) | −4.35887 | −0.413726 | ||||||||
\(112\) | 0.385909 | 0.0364650 | ||||||||
\(113\) | −8.28441 | −0.779332 | −0.389666 | − | 0.920956i | \(-0.627410\pi\) | ||||
−0.389666 | + | 0.920956i | \(0.627410\pi\) | |||||||
\(114\) | 1.86492 | 0.174666 | ||||||||
\(115\) | 21.0971 | 1.96732 | ||||||||
\(116\) | 11.1493 | 1.03519 | ||||||||
\(117\) | −7.15655 | −0.661623 | ||||||||
\(118\) | −8.16353 | −0.751514 | ||||||||
\(119\) | 12.2152 | 1.11976 | ||||||||
\(120\) | 21.7133 | 1.98214 | ||||||||
\(121\) | −9.66115 | −0.878286 | ||||||||
\(122\) | 5.35452 | 0.484776 | ||||||||
\(123\) | −7.30726 | −0.658873 | ||||||||
\(124\) | 1.95202 | 0.175296 | ||||||||
\(125\) | −11.6982 | −1.04632 | ||||||||
\(126\) | 3.14675 | 0.280335 | ||||||||
\(127\) | −11.1304 | −0.987664 | −0.493832 | − | 0.869557i | \(-0.664404\pi\) | ||||
−0.493832 | + | 0.869557i | \(0.664404\pi\) | |||||||
\(128\) | 6.45178 | 0.570262 | ||||||||
\(129\) | −15.3175 | −1.34863 | ||||||||
\(130\) | −17.0726 | −1.49736 | ||||||||
\(131\) | −10.8833 | −0.950879 | −0.475440 | − | 0.879748i | \(-0.657711\pi\) | ||||
−0.475440 | + | 0.879748i | \(0.657711\pi\) | |||||||
\(132\) | −2.90561 | −0.252901 | ||||||||
\(133\) | −2.58906 | −0.224500 | ||||||||
\(134\) | −3.30354 | −0.285383 | ||||||||
\(135\) | −12.4438 | −1.07099 | ||||||||
\(136\) | −13.4932 | −1.15703 | ||||||||
\(137\) | −1.22392 | −0.104567 | −0.0522833 | − | 0.998632i | \(-0.516650\pi\) | ||||
−0.0522833 | + | 0.998632i | \(0.516650\pi\) | |||||||
\(138\) | −10.8220 | −0.921229 | ||||||||
\(139\) | −13.2395 | −1.12296 | −0.561479 | − | 0.827491i | \(-0.689768\pi\) | ||||
−0.561479 | + | 0.827491i | \(0.689768\pi\) | |||||||
\(140\) | −11.3188 | −0.956611 | ||||||||
\(141\) | −12.4962 | −1.05237 | ||||||||
\(142\) | 1.59399 | 0.133765 | ||||||||
\(143\) | 6.08441 | 0.508804 | ||||||||
\(144\) | −0.202859 | −0.0169049 | ||||||||
\(145\) | 33.7089 | 2.79937 | ||||||||
\(146\) | 4.91403 | 0.406688 | ||||||||
\(147\) | 0.619754 | 0.0511164 | ||||||||
\(148\) | −2.50994 | −0.206315 | ||||||||
\(149\) | −2.76637 | −0.226630 | −0.113315 | − | 0.993559i | \(-0.536147\pi\) | ||||
−0.113315 | + | 0.993559i | \(0.536147\pi\) | |||||||
\(150\) | 15.3253 | 1.25131 | ||||||||
\(151\) | −0.300056 | −0.0244182 | −0.0122091 | − | 0.999925i | \(-0.503886\pi\) | ||||
−0.0122091 | + | 0.999925i | \(0.503886\pi\) | |||||||
\(152\) | 2.85994 | 0.231971 | ||||||||
\(153\) | −6.42110 | −0.519115 | ||||||||
\(154\) | −2.67533 | −0.215584 | ||||||||
\(155\) | 5.90175 | 0.474040 | ||||||||
\(156\) | −13.2046 | −1.05721 | ||||||||
\(157\) | 15.5334 | 1.23970 | 0.619849 | − | 0.784721i | \(-0.287194\pi\) | ||||
0.619849 | + | 0.784721i | \(0.287194\pi\) | |||||||
\(158\) | −3.95212 | −0.314414 | ||||||||
\(159\) | −12.4724 | −0.989128 | ||||||||
\(160\) | 20.3113 | 1.60575 | ||||||||
\(161\) | 15.0241 | 1.18406 | ||||||||
\(162\) | 10.0294 | 0.787984 | ||||||||
\(163\) | −5.38699 | −0.421942 | −0.210971 | − | 0.977492i | \(-0.567663\pi\) | ||||
−0.210971 | + | 0.977492i | \(0.567663\pi\) | |||||||
\(164\) | −4.20768 | −0.328564 | ||||||||
\(165\) | −8.78487 | −0.683901 | ||||||||
\(166\) | −13.1997 | −1.02450 | ||||||||
\(167\) | 16.4343 | 1.27173 | 0.635863 | − | 0.771802i | \(-0.280644\pi\) | ||||
0.635863 | + | 0.771802i | \(0.280644\pi\) | |||||||
\(168\) | 15.4629 | 1.19299 | ||||||||
\(169\) | 14.6507 | 1.12697 | ||||||||
\(170\) | −15.3181 | −1.17484 | ||||||||
\(171\) | 1.36098 | 0.104077 | ||||||||
\(172\) | −8.82014 | −0.672529 | ||||||||
\(173\) | 18.1456 | 1.37959 | 0.689794 | − | 0.724006i | \(-0.257701\pi\) | ||||
0.689794 | + | 0.724006i | \(0.257701\pi\) | |||||||
\(174\) | −17.2913 | −1.31085 | ||||||||
\(175\) | −21.2760 | −1.60832 | ||||||||
\(176\) | 0.172468 | 0.0130003 | ||||||||
\(177\) | −19.0898 | −1.43488 | ||||||||
\(178\) | −1.33986 | −0.100426 | ||||||||
\(179\) | −6.32716 | −0.472914 | −0.236457 | − | 0.971642i | \(-0.575986\pi\) | ||||
−0.236457 | + | 0.971642i | \(0.575986\pi\) | |||||||
\(180\) | 5.94988 | 0.443478 | ||||||||
\(181\) | −7.44417 | −0.553321 | −0.276660 | − | 0.960968i | \(-0.589228\pi\) | ||||
−0.276660 | + | 0.960968i | \(0.589228\pi\) | |||||||
\(182\) | −12.1580 | −0.901214 | ||||||||
\(183\) | 12.5211 | 0.925589 | ||||||||
\(184\) | −16.5960 | −1.22347 | ||||||||
\(185\) | −7.58857 | −0.557923 | ||||||||
\(186\) | −3.02736 | −0.221977 | ||||||||
\(187\) | 5.45914 | 0.399212 | ||||||||
\(188\) | −7.19558 | −0.524791 | ||||||||
\(189\) | −8.86174 | −0.644596 | ||||||||
\(190\) | 3.24673 | 0.235543 | ||||||||
\(191\) | −24.3366 | −1.76093 | −0.880467 | − | 0.474107i | \(-0.842771\pi\) | ||||
−0.880467 | + | 0.474107i | \(0.842771\pi\) | |||||||
\(192\) | −11.0414 | −0.796846 | ||||||||
\(193\) | 24.4987 | 1.76345 | 0.881726 | − | 0.471761i | \(-0.156381\pi\) | ||||
0.881726 | + | 0.471761i | \(0.156381\pi\) | |||||||
\(194\) | −9.11532 | −0.654442 | ||||||||
\(195\) | −39.9229 | −2.85894 | ||||||||
\(196\) | 0.356868 | 0.0254906 | ||||||||
\(197\) | 3.27248 | 0.233154 | 0.116577 | − | 0.993182i | \(-0.462808\pi\) | ||||
0.116577 | + | 0.993182i | \(0.462808\pi\) | |||||||
\(198\) | 1.40633 | 0.0999432 | ||||||||
\(199\) | −20.7297 | −1.46949 | −0.734743 | − | 0.678346i | \(-0.762697\pi\) | ||||
−0.734743 | + | 0.678346i | \(0.762697\pi\) | |||||||
\(200\) | 23.5020 | 1.66184 | ||||||||
\(201\) | −7.72508 | −0.544885 | ||||||||
\(202\) | 8.63566 | 0.607603 | ||||||||
\(203\) | 24.0054 | 1.68485 | ||||||||
\(204\) | −11.8476 | −0.829498 | ||||||||
\(205\) | −12.7215 | −0.888511 | ||||||||
\(206\) | −13.2303 | −0.921796 | ||||||||
\(207\) | −7.89763 | −0.548923 | ||||||||
\(208\) | 0.783784 | 0.0543456 | ||||||||
\(209\) | −1.15709 | −0.0800374 | ||||||||
\(210\) | 17.5542 | 1.21135 | ||||||||
\(211\) | 1.00000 | 0.0688428 | ||||||||
\(212\) | −7.18190 | −0.493255 | ||||||||
\(213\) | 3.72742 | 0.255398 | ||||||||
\(214\) | 12.0696 | 0.825063 | ||||||||
\(215\) | −26.6669 | −1.81867 | ||||||||
\(216\) | 9.78889 | 0.666049 | ||||||||
\(217\) | 4.20286 | 0.285309 | ||||||||
\(218\) | −10.8098 | −0.732134 | ||||||||
\(219\) | 11.4911 | 0.776495 | ||||||||
\(220\) | −5.05852 | −0.341045 | ||||||||
\(221\) | 24.8091 | 1.66884 | ||||||||
\(222\) | 3.89263 | 0.261256 | ||||||||
\(223\) | 14.8445 | 0.994064 | 0.497032 | − | 0.867732i | \(-0.334423\pi\) | ||||
0.497032 | + | 0.867732i | \(0.334423\pi\) | |||||||
\(224\) | 14.4645 | 0.966447 | ||||||||
\(225\) | 11.1841 | 0.745604 | ||||||||
\(226\) | 7.39828 | 0.492126 | ||||||||
\(227\) | −22.9605 | −1.52394 | −0.761972 | − | 0.647610i | \(-0.775769\pi\) | ||||
−0.761972 | + | 0.647610i | \(0.775769\pi\) | |||||||
\(228\) | 2.51115 | 0.166305 | ||||||||
\(229\) | −20.3046 | −1.34176 | −0.670882 | − | 0.741564i | \(-0.734084\pi\) | ||||
−0.670882 | + | 0.741564i | \(0.734084\pi\) | |||||||
\(230\) | −18.8405 | −1.24231 | ||||||||
\(231\) | −6.25604 | −0.411617 | ||||||||
\(232\) | −26.5169 | −1.74092 | ||||||||
\(233\) | −3.19355 | −0.209217 | −0.104608 | − | 0.994513i | \(-0.533359\pi\) | ||||
−0.104608 | + | 0.994513i | \(0.533359\pi\) | |||||||
\(234\) | 6.39106 | 0.417796 | ||||||||
\(235\) | −21.7552 | −1.41915 | ||||||||
\(236\) | −10.9923 | −0.715539 | ||||||||
\(237\) | −9.24173 | −0.600315 | ||||||||
\(238\) | −10.9086 | −0.707100 | ||||||||
\(239\) | 10.0855 | 0.652374 | 0.326187 | − | 0.945305i | \(-0.394236\pi\) | ||||
0.326187 | + | 0.945305i | \(0.394236\pi\) | |||||||
\(240\) | −1.13165 | −0.0730478 | ||||||||
\(241\) | −8.46605 | −0.545346 | −0.272673 | − | 0.962107i | \(-0.587908\pi\) | ||||
−0.272673 | + | 0.962107i | \(0.587908\pi\) | |||||||
\(242\) | 8.62776 | 0.554613 | ||||||||
\(243\) | 13.1847 | 0.845797 | ||||||||
\(244\) | 7.20994 | 0.461569 | ||||||||
\(245\) | 1.07896 | 0.0689321 | ||||||||
\(246\) | 6.52564 | 0.416060 | ||||||||
\(247\) | −5.25839 | −0.334583 | ||||||||
\(248\) | −4.64258 | −0.294804 | ||||||||
\(249\) | −30.8666 | −1.95609 | ||||||||
\(250\) | 10.4469 | 0.660720 | ||||||||
\(251\) | 8.08792 | 0.510505 | 0.255253 | − | 0.966874i | \(-0.417841\pi\) | ||||
0.255253 | + | 0.966874i | \(0.417841\pi\) | |||||||
\(252\) | 4.23714 | 0.266915 | ||||||||
\(253\) | 6.71447 | 0.422135 | ||||||||
\(254\) | 9.93985 | 0.623682 | ||||||||
\(255\) | −35.8202 | −2.24315 | ||||||||
\(256\) | −16.3363 | −1.02102 | ||||||||
\(257\) | −18.9026 | −1.17911 | −0.589556 | − | 0.807728i | \(-0.700697\pi\) | ||||
−0.589556 | + | 0.807728i | \(0.700697\pi\) | |||||||
\(258\) | 13.6791 | 0.851621 | ||||||||
\(259\) | −5.40411 | −0.335795 | ||||||||
\(260\) | −22.9885 | −1.42568 | ||||||||
\(261\) | −12.6188 | −0.781084 | ||||||||
\(262\) | 9.71919 | 0.600454 | ||||||||
\(263\) | 0.398805 | 0.0245914 | 0.0122957 | − | 0.999924i | \(-0.496086\pi\) | ||||
0.0122957 | + | 0.999924i | \(0.496086\pi\) | |||||||
\(264\) | 6.91058 | 0.425317 | ||||||||
\(265\) | −21.7138 | −1.33387 | ||||||||
\(266\) | 2.31212 | 0.141765 | ||||||||
\(267\) | −3.13315 | −0.191746 | ||||||||
\(268\) | −4.44827 | −0.271721 | ||||||||
\(269\) | 10.6158 | 0.647255 | 0.323627 | − | 0.946185i | \(-0.395098\pi\) | ||||
0.323627 | + | 0.946185i | \(0.395098\pi\) | |||||||
\(270\) | 11.1128 | 0.676303 | ||||||||
\(271\) | 13.7579 | 0.835731 | 0.417865 | − | 0.908509i | \(-0.362778\pi\) | ||||
0.417865 | + | 0.908509i | \(0.362778\pi\) | |||||||
\(272\) | 0.703237 | 0.0426400 | ||||||||
\(273\) | −28.4306 | −1.72070 | ||||||||
\(274\) | 1.09301 | 0.0660309 | ||||||||
\(275\) | −9.50855 | −0.573387 | ||||||||
\(276\) | −14.5720 | −0.877129 | ||||||||
\(277\) | −14.5666 | −0.875223 | −0.437612 | − | 0.899164i | \(-0.644176\pi\) | ||||
−0.437612 | + | 0.899164i | \(0.644176\pi\) | |||||||
\(278\) | 11.8233 | 0.709117 | ||||||||
\(279\) | −2.20930 | −0.132267 | ||||||||
\(280\) | 26.9200 | 1.60878 | ||||||||
\(281\) | 18.5659 | 1.10755 | 0.553773 | − | 0.832667i | \(-0.313187\pi\) | ||||
0.553773 | + | 0.832667i | \(0.313187\pi\) | |||||||
\(282\) | 11.1595 | 0.664541 | ||||||||
\(283\) | 3.31199 | 0.196877 | 0.0984386 | − | 0.995143i | \(-0.468615\pi\) | ||||
0.0984386 | + | 0.995143i | \(0.468615\pi\) | |||||||
\(284\) | 2.14633 | 0.127361 | ||||||||
\(285\) | 7.59223 | 0.449725 | ||||||||
\(286\) | −5.43360 | −0.321296 | ||||||||
\(287\) | −9.05950 | −0.534765 | ||||||||
\(288\) | −7.60346 | −0.448038 | ||||||||
\(289\) | 5.25958 | 0.309387 | ||||||||
\(290\) | −30.1033 | −1.76772 | ||||||||
\(291\) | −21.3155 | −1.24953 | ||||||||
\(292\) | 6.61681 | 0.387220 | ||||||||
\(293\) | 5.43984 | 0.317799 | 0.158899 | − | 0.987295i | \(-0.449205\pi\) | ||||
0.158899 | + | 0.987295i | \(0.449205\pi\) | |||||||
\(294\) | −0.553463 | −0.0322786 | ||||||||
\(295\) | −33.2343 | −1.93498 | ||||||||
\(296\) | 5.96951 | 0.346971 | ||||||||
\(297\) | −3.96043 | −0.229808 | ||||||||
\(298\) | 2.47047 | 0.143111 | ||||||||
\(299\) | 30.5140 | 1.76467 | ||||||||
\(300\) | 20.6358 | 1.19141 | ||||||||
\(301\) | −18.9905 | −1.09460 | ||||||||
\(302\) | 0.267961 | 0.0154194 | ||||||||
\(303\) | 20.1938 | 1.16010 | ||||||||
\(304\) | −0.149054 | −0.00854883 | ||||||||
\(305\) | 21.7986 | 1.24819 | ||||||||
\(306\) | 5.73427 | 0.327807 | ||||||||
\(307\) | 23.0389 | 1.31490 | 0.657449 | − | 0.753499i | \(-0.271635\pi\) | ||||
0.657449 | + | 0.753499i | \(0.271635\pi\) | |||||||
\(308\) | −3.60237 | −0.205264 | ||||||||
\(309\) | −30.9379 | −1.76000 | ||||||||
\(310\) | −5.27047 | −0.299343 | ||||||||
\(311\) | −6.99870 | −0.396860 | −0.198430 | − | 0.980115i | \(-0.563584\pi\) | ||||
−0.198430 | + | 0.980115i | \(0.563584\pi\) | |||||||
\(312\) | 31.4052 | 1.77797 | ||||||||
\(313\) | −23.2253 | −1.31277 | −0.656385 | − | 0.754426i | \(-0.727915\pi\) | ||||
−0.656385 | + | 0.754426i | \(0.727915\pi\) | |||||||
\(314\) | −13.8719 | −0.782835 | ||||||||
\(315\) | 12.8106 | 0.721797 | ||||||||
\(316\) | −5.32159 | −0.299363 | ||||||||
\(317\) | 10.2293 | 0.574533 | 0.287267 | − | 0.957851i | \(-0.407253\pi\) | ||||
0.287267 | + | 0.957851i | \(0.407253\pi\) | |||||||
\(318\) | 11.1383 | 0.624607 | ||||||||
\(319\) | 10.7284 | 0.600672 | ||||||||
\(320\) | −19.2225 | −1.07457 | ||||||||
\(321\) | 28.2239 | 1.57530 | ||||||||
\(322\) | −13.4170 | −0.747703 | ||||||||
\(323\) | −4.71801 | −0.262517 | ||||||||
\(324\) | 13.5047 | 0.750263 | ||||||||
\(325\) | −43.2117 | −2.39695 | ||||||||
\(326\) | 4.81078 | 0.266444 | ||||||||
\(327\) | −25.2779 | −1.39787 | ||||||||
\(328\) | 10.0073 | 0.552563 | ||||||||
\(329\) | −15.4927 | −0.854141 | ||||||||
\(330\) | 7.84521 | 0.431864 | ||||||||
\(331\) | 4.46663 | 0.245508 | 0.122754 | − | 0.992437i | \(-0.460827\pi\) | ||||
0.122754 | + | 0.992437i | \(0.460827\pi\) | |||||||
\(332\) | −17.7736 | −0.975456 | ||||||||
\(333\) | 2.84075 | 0.155672 | ||||||||
\(334\) | −14.6764 | −0.803059 | ||||||||
\(335\) | −13.4490 | −0.734795 | ||||||||
\(336\) | −0.805893 | −0.0439651 | ||||||||
\(337\) | −29.5396 | −1.60913 | −0.804563 | − | 0.593868i | \(-0.797600\pi\) | ||||
−0.804563 | + | 0.593868i | \(0.797600\pi\) | |||||||
\(338\) | −13.0836 | −0.711652 | ||||||||
\(339\) | 17.3003 | 0.939623 | ||||||||
\(340\) | −20.6260 | −1.11860 | ||||||||
\(341\) | 1.87832 | 0.101717 | ||||||||
\(342\) | −1.21540 | −0.0657214 | ||||||||
\(343\) | 18.8918 | 1.02006 | ||||||||
\(344\) | 20.9774 | 1.13103 | ||||||||
\(345\) | −44.0570 | −2.37195 | ||||||||
\(346\) | −16.2047 | −0.871171 | ||||||||
\(347\) | −27.4734 | −1.47485 | −0.737424 | − | 0.675430i | \(-0.763958\pi\) | ||||
−0.737424 | + | 0.675430i | \(0.763958\pi\) | |||||||
\(348\) | −23.2830 | −1.24810 | ||||||||
\(349\) | 11.6487 | 0.623539 | 0.311769 | − | 0.950158i | \(-0.399078\pi\) | ||||
0.311769 | + | 0.950158i | \(0.399078\pi\) | |||||||
\(350\) | 19.0003 | 1.01561 | ||||||||
\(351\) | −17.9982 | −0.960674 | ||||||||
\(352\) | 6.46437 | 0.344552 | ||||||||
\(353\) | 36.7989 | 1.95861 | 0.979303 | − | 0.202399i | \(-0.0648737\pi\) | ||||
0.979303 | + | 0.202399i | \(0.0648737\pi\) | |||||||
\(354\) | 17.0479 | 0.906084 | ||||||||
\(355\) | 6.48923 | 0.344413 | ||||||||
\(356\) | −1.80414 | −0.0956190 | ||||||||
\(357\) | −25.5089 | −1.35008 | ||||||||
\(358\) | 5.65038 | 0.298632 | ||||||||
\(359\) | −25.9133 | −1.36765 | −0.683827 | − | 0.729644i | \(-0.739686\pi\) | ||||
−0.683827 | + | 0.729644i | \(0.739686\pi\) | |||||||
\(360\) | −14.1509 | −0.745819 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 6.64791 | 0.349406 | ||||||||
\(363\) | 20.1753 | 1.05893 | ||||||||
\(364\) | −16.3710 | −0.858073 | ||||||||
\(365\) | 20.0053 | 1.04713 | ||||||||
\(366\) | −11.1818 | −0.584483 | ||||||||
\(367\) | 25.8156 | 1.34756 | 0.673782 | − | 0.738930i | \(-0.264669\pi\) | ||||
0.673782 | + | 0.738930i | \(0.264669\pi\) | |||||||
\(368\) | 0.864947 | 0.0450885 | ||||||||
\(369\) | 4.76226 | 0.247913 | ||||||||
\(370\) | 6.77687 | 0.352312 | ||||||||
\(371\) | −15.4633 | −0.802812 | ||||||||
\(372\) | −4.07638 | −0.211351 | ||||||||
\(373\) | −9.65684 | −0.500012 | −0.250006 | − | 0.968244i | \(-0.580433\pi\) | ||||
−0.250006 | + | 0.968244i | \(0.580433\pi\) | |||||||
\(374\) | −4.87521 | −0.252091 | ||||||||
\(375\) | 24.4293 | 1.26152 | ||||||||
\(376\) | 17.1136 | 0.882567 | ||||||||
\(377\) | 48.7551 | 2.51101 | ||||||||
\(378\) | 7.91385 | 0.407045 | ||||||||
\(379\) | 24.5808 | 1.26263 | 0.631315 | − | 0.775527i | \(-0.282516\pi\) | ||||
0.631315 | + | 0.775527i | \(0.282516\pi\) | |||||||
\(380\) | 4.37177 | 0.224267 | ||||||||
\(381\) | 23.2436 | 1.19080 | ||||||||
\(382\) | 21.7335 | 1.11198 | ||||||||
\(383\) | −18.0944 | −0.924580 | −0.462290 | − | 0.886729i | \(-0.652972\pi\) | ||||
−0.462290 | + | 0.886729i | \(0.652972\pi\) | |||||||
\(384\) | −13.4732 | −0.687553 | ||||||||
\(385\) | −10.8914 | −0.555079 | ||||||||
\(386\) | −21.8782 | −1.11357 | ||||||||
\(387\) | 9.98266 | 0.507447 | ||||||||
\(388\) | −12.2739 | −0.623113 | ||||||||
\(389\) | −4.69382 | −0.237986 | −0.118993 | − | 0.992895i | \(-0.537967\pi\) | ||||
−0.118993 | + | 0.992895i | \(0.537967\pi\) | |||||||
\(390\) | 35.6526 | 1.80534 | ||||||||
\(391\) | 27.3782 | 1.38457 | ||||||||
\(392\) | −0.848758 | −0.0428687 | ||||||||
\(393\) | 22.7276 | 1.14645 | ||||||||
\(394\) | −2.92244 | −0.147230 | ||||||||
\(395\) | −16.0894 | −0.809544 | ||||||||
\(396\) | 1.89364 | 0.0951589 | ||||||||
\(397\) | 8.52553 | 0.427884 | 0.213942 | − | 0.976846i | \(-0.431370\pi\) | ||||
0.213942 | + | 0.976846i | \(0.431370\pi\) | |||||||
\(398\) | 18.5123 | 0.927939 | ||||||||
\(399\) | 5.40672 | 0.270675 | ||||||||
\(400\) | −1.22488 | −0.0612438 | ||||||||
\(401\) | 15.1496 | 0.756533 | 0.378266 | − | 0.925697i | \(-0.376520\pi\) | ||||
0.378266 | + | 0.925697i | \(0.376520\pi\) | |||||||
\(402\) | 6.89878 | 0.344080 | ||||||||
\(403\) | 8.53603 | 0.425210 | ||||||||
\(404\) | 11.6280 | 0.578517 | ||||||||
\(405\) | 40.8304 | 2.02888 | ||||||||
\(406\) | −21.4377 | −1.06393 | ||||||||
\(407\) | −2.41517 | −0.119716 | ||||||||
\(408\) | 28.1778 | 1.39501 | ||||||||
\(409\) | 34.9914 | 1.73021 | 0.865107 | − | 0.501588i | \(-0.167251\pi\) | ||||
0.865107 | + | 0.501588i | \(0.167251\pi\) | |||||||
\(410\) | 11.3608 | 0.561070 | ||||||||
\(411\) | 2.55591 | 0.126074 | ||||||||
\(412\) | −17.8147 | −0.877669 | ||||||||
\(413\) | −23.6674 | −1.16460 | ||||||||
\(414\) | 7.05287 | 0.346630 | ||||||||
\(415\) | −53.7370 | −2.63785 | ||||||||
\(416\) | 29.3774 | 1.44034 | ||||||||
\(417\) | 27.6480 | 1.35393 | ||||||||
\(418\) | 1.03332 | 0.0505414 | ||||||||
\(419\) | 17.2771 | 0.844042 | 0.422021 | − | 0.906586i | \(-0.361321\pi\) | ||||
0.422021 | + | 0.906586i | \(0.361321\pi\) | |||||||
\(420\) | 23.6369 | 1.15336 | ||||||||
\(421\) | 9.62989 | 0.469332 | 0.234666 | − | 0.972076i | \(-0.424600\pi\) | ||||
0.234666 | + | 0.972076i | \(0.424600\pi\) | |||||||
\(422\) | −0.893036 | −0.0434723 | ||||||||
\(423\) | 8.14397 | 0.395974 | ||||||||
\(424\) | 17.0811 | 0.829531 | ||||||||
\(425\) | −38.7710 | −1.88067 | ||||||||
\(426\) | −3.32872 | −0.161277 | ||||||||
\(427\) | 15.5236 | 0.751242 | ||||||||
\(428\) | 16.2519 | 0.785567 | ||||||||
\(429\) | −12.7061 | −0.613454 | ||||||||
\(430\) | 23.8145 | 1.14844 | ||||||||
\(431\) | −25.2632 | −1.21689 | −0.608443 | − | 0.793598i | \(-0.708205\pi\) | ||||
−0.608443 | + | 0.793598i | \(0.708205\pi\) | |||||||
\(432\) | −0.510176 | −0.0245459 | ||||||||
\(433\) | 12.6048 | 0.605747 | 0.302874 | − | 0.953031i | \(-0.402054\pi\) | ||||
0.302874 | + | 0.953031i | \(0.402054\pi\) | |||||||
\(434\) | −3.75331 | −0.180164 | ||||||||
\(435\) | −70.3941 | −3.37514 | ||||||||
\(436\) | −14.5556 | −0.697087 | ||||||||
\(437\) | −5.80291 | −0.277591 | ||||||||
\(438\) | −10.2619 | −0.490335 | ||||||||
\(439\) | −0.465354 | −0.0222101 | −0.0111051 | − | 0.999938i | \(-0.503535\pi\) | ||||
−0.0111051 | + | 0.999938i | \(0.503535\pi\) | |||||||
\(440\) | 12.0309 | 0.573553 | ||||||||
\(441\) | −0.403904 | −0.0192335 | ||||||||
\(442\) | −22.1554 | −1.05383 | ||||||||
\(443\) | 28.9952 | 1.37761 | 0.688803 | − | 0.724949i | \(-0.258137\pi\) | ||||
0.688803 | + | 0.724949i | \(0.258137\pi\) | |||||||
\(444\) | 5.24149 | 0.248750 | ||||||||
\(445\) | −5.45465 | −0.258575 | ||||||||
\(446\) | −13.2567 | −0.627724 | ||||||||
\(447\) | 5.77700 | 0.273243 | ||||||||
\(448\) | −13.6891 | −0.646749 | ||||||||
\(449\) | −29.8561 | −1.40900 | −0.704498 | − | 0.709706i | \(-0.748828\pi\) | ||||
−0.704498 | + | 0.709706i | \(0.748828\pi\) | |||||||
\(450\) | −9.98777 | −0.470828 | ||||||||
\(451\) | −4.04882 | −0.190651 | ||||||||
\(452\) | 9.96189 | 0.468568 | ||||||||
\(453\) | 0.626606 | 0.0294405 | ||||||||
\(454\) | 20.5046 | 0.962328 | ||||||||
\(455\) | −49.4962 | −2.32042 | ||||||||
\(456\) | −5.97239 | −0.279683 | ||||||||
\(457\) | 35.5833 | 1.66452 | 0.832259 | − | 0.554387i | \(-0.187047\pi\) | ||||
0.832259 | + | 0.554387i | \(0.187047\pi\) | |||||||
\(458\) | 18.1327 | 0.847287 | ||||||||
\(459\) | −16.1486 | −0.753753 | ||||||||
\(460\) | −25.3690 | −1.18284 | ||||||||
\(461\) | −1.55313 | −0.0723363 | −0.0361681 | − | 0.999346i | \(-0.511515\pi\) | ||||
−0.0361681 | + | 0.999346i | \(0.511515\pi\) | |||||||
\(462\) | 5.58687 | 0.259925 | ||||||||
\(463\) | 1.73303 | 0.0805407 | 0.0402703 | − | 0.999189i | \(-0.487178\pi\) | ||||
0.0402703 | + | 0.999189i | \(0.487178\pi\) | |||||||
\(464\) | 1.38201 | 0.0641581 | ||||||||
\(465\) | −12.3246 | −0.571539 | ||||||||
\(466\) | 2.85196 | 0.132114 | ||||||||
\(467\) | 28.7920 | 1.33233 | 0.666167 | − | 0.745802i | \(-0.267934\pi\) | ||||
0.666167 | + | 0.745802i | \(0.267934\pi\) | |||||||
\(468\) | 8.60565 | 0.397796 | ||||||||
\(469\) | −9.57752 | −0.442249 | ||||||||
\(470\) | 19.4282 | 0.896155 | ||||||||
\(471\) | −32.4383 | −1.49468 | ||||||||
\(472\) | 26.1436 | 1.20336 | ||||||||
\(473\) | −8.48714 | −0.390239 | ||||||||
\(474\) | 8.25320 | 0.379082 | ||||||||
\(475\) | 8.21767 | 0.377052 | ||||||||
\(476\) | −14.6886 | −0.673251 | ||||||||
\(477\) | 8.12849 | 0.372178 | ||||||||
\(478\) | −9.00668 | −0.411956 | ||||||||
\(479\) | 6.72157 | 0.307117 | 0.153558 | − | 0.988140i | \(-0.450927\pi\) | ||||
0.153558 | + | 0.988140i | \(0.450927\pi\) | |||||||
\(480\) | −42.4160 | −1.93602 | ||||||||
\(481\) | −10.9758 | −0.500452 | ||||||||
\(482\) | 7.56049 | 0.344371 | ||||||||
\(483\) | −31.3747 | −1.42760 | ||||||||
\(484\) | 11.6174 | 0.528064 | ||||||||
\(485\) | −37.1091 | −1.68504 | ||||||||
\(486\) | −11.7744 | −0.534097 | ||||||||
\(487\) | −28.1002 | −1.27334 | −0.636671 | − | 0.771136i | \(-0.719689\pi\) | ||||
−0.636671 | + | 0.771136i | \(0.719689\pi\) | |||||||
\(488\) | −17.1478 | −0.776244 | ||||||||
\(489\) | 11.2496 | 0.508726 | ||||||||
\(490\) | −0.963549 | −0.0435287 | ||||||||
\(491\) | 5.59129 | 0.252332 | 0.126166 | − | 0.992009i | \(-0.459733\pi\) | ||||
0.126166 | + | 0.992009i | \(0.459733\pi\) | |||||||
\(492\) | 8.78687 | 0.396143 | ||||||||
\(493\) | 43.7447 | 1.97016 | ||||||||
\(494\) | 4.69593 | 0.211280 | ||||||||
\(495\) | 5.72525 | 0.257331 | ||||||||
\(496\) | 0.241962 | 0.0108644 | ||||||||
\(497\) | 4.62123 | 0.207291 | ||||||||
\(498\) | 27.5650 | 1.23522 | ||||||||
\(499\) | 23.4167 | 1.04828 | 0.524139 | − | 0.851633i | \(-0.324387\pi\) | ||||
0.524139 | + | 0.851633i | \(0.324387\pi\) | |||||||
\(500\) | 14.0669 | 0.629091 | ||||||||
\(501\) | −34.3197 | −1.53329 | ||||||||
\(502\) | −7.22281 | −0.322370 | ||||||||
\(503\) | −25.8124 | −1.15092 | −0.575459 | − | 0.817831i | \(-0.695176\pi\) | ||||
−0.575459 | + | 0.817831i | \(0.695176\pi\) | |||||||
\(504\) | −10.0774 | −0.448884 | ||||||||
\(505\) | 35.1564 | 1.56444 | ||||||||
\(506\) | −5.99627 | −0.266567 | ||||||||
\(507\) | −30.5949 | −1.35877 | ||||||||
\(508\) | 13.3842 | 0.593826 | ||||||||
\(509\) | −23.5181 | −1.04242 | −0.521212 | − | 0.853427i | \(-0.674520\pi\) | ||||
−0.521212 | + | 0.853427i | \(0.674520\pi\) | |||||||
\(510\) | 31.9887 | 1.41648 | ||||||||
\(511\) | 14.2466 | 0.630231 | ||||||||
\(512\) | 1.68530 | 0.0744804 | ||||||||
\(513\) | 3.42276 | 0.151119 | ||||||||
\(514\) | 16.8807 | 0.744576 | ||||||||
\(515\) | −53.8613 | −2.37341 | ||||||||
\(516\) | 18.4191 | 0.810854 | ||||||||
\(517\) | −6.92391 | −0.304513 | ||||||||
\(518\) | 4.82607 | 0.212045 | ||||||||
\(519\) | −37.8935 | −1.66334 | ||||||||
\(520\) | 54.6747 | 2.39764 | ||||||||
\(521\) | 16.2908 | 0.713715 | 0.356858 | − | 0.934159i | \(-0.383848\pi\) | ||||
0.356858 | + | 0.934159i | \(0.383848\pi\) | |||||||
\(522\) | 11.2690 | 0.493233 | ||||||||
\(523\) | 4.22810 | 0.184882 | 0.0924410 | − | 0.995718i | \(-0.470533\pi\) | ||||
0.0924410 | + | 0.995718i | \(0.470533\pi\) | |||||||
\(524\) | 13.0870 | 0.571710 | ||||||||
\(525\) | 44.4306 | 1.93911 | ||||||||
\(526\) | −0.356147 | −0.0155288 | ||||||||
\(527\) | 7.65881 | 0.333623 | ||||||||
\(528\) | −0.360165 | −0.0156742 | ||||||||
\(529\) | 10.6738 | 0.464078 | ||||||||
\(530\) | 19.3912 | 0.842302 | ||||||||
\(531\) | 12.4411 | 0.539899 | ||||||||
\(532\) | 3.11331 | 0.134979 | ||||||||
\(533\) | −18.3999 | −0.796987 | ||||||||
\(534\) | 2.79802 | 0.121082 | ||||||||
\(535\) | 49.1363 | 2.12435 | ||||||||
\(536\) | 10.5796 | 0.456967 | ||||||||
\(537\) | 13.2130 | 0.570182 | ||||||||
\(538\) | −9.48026 | −0.408723 | ||||||||
\(539\) | 0.343394 | 0.0147910 | ||||||||
\(540\) | 14.9635 | 0.643928 | ||||||||
\(541\) | 13.4238 | 0.577133 | 0.288567 | − | 0.957460i | \(-0.406821\pi\) | ||||
0.288567 | + | 0.957460i | \(0.406821\pi\) | |||||||
\(542\) | −12.2863 | −0.527741 | ||||||||
\(543\) | 15.5456 | 0.667126 | ||||||||
\(544\) | 26.3584 | 1.13011 | ||||||||
\(545\) | −44.0076 | −1.88508 | ||||||||
\(546\) | 25.3896 | 1.08657 | ||||||||
\(547\) | 17.8070 | 0.761371 | 0.380685 | − | 0.924705i | \(-0.375688\pi\) | ||||
0.380685 | + | 0.924705i | \(0.375688\pi\) | |||||||
\(548\) | 1.47175 | 0.0628699 | ||||||||
\(549\) | −8.16023 | −0.348270 | ||||||||
\(550\) | 8.49148 | 0.362078 | ||||||||
\(551\) | −9.27186 | −0.394995 | ||||||||
\(552\) | 34.6573 | 1.47511 | ||||||||
\(553\) | −11.4579 | −0.487238 | ||||||||
\(554\) | 13.0085 | 0.552679 | ||||||||
\(555\) | 15.8472 | 0.672675 | ||||||||
\(556\) | 15.9203 | 0.675171 | ||||||||
\(557\) | −41.7680 | −1.76977 | −0.884884 | − | 0.465812i | \(-0.845762\pi\) | ||||
−0.884884 | + | 0.465812i | \(0.845762\pi\) | |||||||
\(558\) | 1.97298 | 0.0835230 | ||||||||
\(559\) | −38.5699 | −1.63133 | ||||||||
\(560\) | −1.40302 | −0.0592883 | ||||||||
\(561\) | −11.4003 | −0.481321 | ||||||||
\(562\) | −16.5800 | −0.699385 | ||||||||
\(563\) | 23.8677 | 1.00590 | 0.502952 | − | 0.864314i | \(-0.332247\pi\) | ||||
0.502952 | + | 0.864314i | \(0.332247\pi\) | |||||||
\(564\) | 15.0265 | 0.632729 | ||||||||
\(565\) | 30.1189 | 1.26711 | ||||||||
\(566\) | −2.95772 | −0.124322 | ||||||||
\(567\) | 29.0769 | 1.22111 | ||||||||
\(568\) | −5.10472 | −0.214190 | ||||||||
\(569\) | 38.1261 | 1.59833 | 0.799165 | − | 0.601111i | \(-0.205275\pi\) | ||||
0.799165 | + | 0.601111i | \(0.205275\pi\) | |||||||
\(570\) | −6.78014 | −0.283989 | ||||||||
\(571\) | −9.87638 | −0.413314 | −0.206657 | − | 0.978413i | \(-0.566258\pi\) | ||||
−0.206657 | + | 0.978413i | \(0.566258\pi\) | |||||||
\(572\) | −7.31642 | −0.305915 | ||||||||
\(573\) | 50.8220 | 2.12312 | ||||||||
\(574\) | 8.09046 | 0.337689 | ||||||||
\(575\) | −47.6864 | −1.98866 | ||||||||
\(576\) | 7.19588 | 0.299828 | ||||||||
\(577\) | −23.6347 | −0.983924 | −0.491962 | − | 0.870617i | \(-0.663720\pi\) | ||||
−0.491962 | + | 0.870617i | \(0.663720\pi\) | |||||||
\(578\) | −4.69699 | −0.195369 | ||||||||
\(579\) | −51.1605 | −2.12616 | ||||||||
\(580\) | −40.5345 | −1.68310 | ||||||||
\(581\) | −38.2682 | −1.58763 | ||||||||
\(582\) | 19.0355 | 0.789046 | ||||||||
\(583\) | −6.91075 | −0.286214 | ||||||||
\(584\) | −15.7371 | −0.651206 | ||||||||
\(585\) | 26.0184 | 1.07573 | ||||||||
\(586\) | −4.85797 | −0.200681 | ||||||||
\(587\) | −4.82609 | −0.199194 | −0.0995971 | − | 0.995028i | \(-0.531755\pi\) | ||||
−0.0995971 | + | 0.995028i | \(0.531755\pi\) | |||||||
\(588\) | −0.745246 | −0.0307334 | ||||||||
\(589\) | −1.62332 | −0.0668876 | ||||||||
\(590\) | 29.6794 | 1.22188 | ||||||||
\(591\) | −6.83390 | −0.281109 | ||||||||
\(592\) | −0.311119 | −0.0127869 | ||||||||
\(593\) | −18.4588 | −0.758011 | −0.379006 | − | 0.925394i | \(-0.623734\pi\) | ||||
−0.379006 | + | 0.925394i | \(0.623734\pi\) | |||||||
\(594\) | 3.53681 | 0.145117 | ||||||||
\(595\) | −44.4097 | −1.82062 | ||||||||
\(596\) | 3.32653 | 0.136260 | ||||||||
\(597\) | 43.2896 | 1.77173 | ||||||||
\(598\) | −27.2501 | −1.11434 | ||||||||
\(599\) | −38.4768 | −1.57212 | −0.786060 | − | 0.618150i | \(-0.787883\pi\) | ||||
−0.786060 | + | 0.618150i | \(0.787883\pi\) | |||||||
\(600\) | −49.0791 | −2.00365 | ||||||||
\(601\) | 6.43726 | 0.262581 | 0.131291 | − | 0.991344i | \(-0.458088\pi\) | ||||
0.131291 | + | 0.991344i | \(0.458088\pi\) | |||||||
\(602\) | 16.9592 | 0.691207 | ||||||||
\(603\) | 5.03457 | 0.205023 | ||||||||
\(604\) | 0.360813 | 0.0146813 | ||||||||
\(605\) | 35.1242 | 1.42800 | ||||||||
\(606\) | −18.0338 | −0.732574 | ||||||||
\(607\) | 3.21905 | 0.130657 | 0.0653285 | − | 0.997864i | \(-0.479190\pi\) | ||||
0.0653285 | + | 0.997864i | \(0.479190\pi\) | |||||||
\(608\) | −5.58676 | −0.226573 | ||||||||
\(609\) | −50.1304 | −2.03138 | ||||||||
\(610\) | −19.4670 | −0.788194 | ||||||||
\(611\) | −31.4658 | −1.27297 | ||||||||
\(612\) | 7.72128 | 0.312114 | ||||||||
\(613\) | 0.795323 | 0.0321228 | 0.0160614 | − | 0.999871i | \(-0.494887\pi\) | ||||
0.0160614 | + | 0.999871i | \(0.494887\pi\) | |||||||
\(614\) | −20.5746 | −0.830322 | ||||||||
\(615\) | 26.5663 | 1.07126 | ||||||||
\(616\) | 8.56770 | 0.345202 | ||||||||
\(617\) | −9.50252 | −0.382557 | −0.191279 | − | 0.981536i | \(-0.561263\pi\) | ||||
−0.191279 | + | 0.981536i | \(0.561263\pi\) | |||||||
\(618\) | 27.6287 | 1.11139 | ||||||||
\(619\) | 14.3260 | 0.575811 | 0.287906 | − | 0.957659i | \(-0.407041\pi\) | ||||
0.287906 | + | 0.957659i | \(0.407041\pi\) | |||||||
\(620\) | −7.09677 | −0.285013 | ||||||||
\(621\) | −19.8620 | −0.797035 | ||||||||
\(622\) | 6.25009 | 0.250606 | ||||||||
\(623\) | −3.88446 | −0.155628 | ||||||||
\(624\) | −1.63677 | −0.0655233 | ||||||||
\(625\) | 1.44170 | 0.0576681 | ||||||||
\(626\) | 20.7410 | 0.828978 | ||||||||
\(627\) | 2.41634 | 0.0964993 | ||||||||
\(628\) | −18.6787 | −0.745360 | ||||||||
\(629\) | −9.84784 | −0.392659 | ||||||||
\(630\) | −11.4403 | −0.455794 | ||||||||
\(631\) | 17.7905 | 0.708229 | 0.354114 | − | 0.935202i | \(-0.384782\pi\) | ||||
0.354114 | + | 0.935202i | \(0.384782\pi\) | |||||||
\(632\) | 12.6566 | 0.503453 | ||||||||
\(633\) | −2.08830 | −0.0830023 | ||||||||
\(634\) | −9.13511 | −0.362802 | ||||||||
\(635\) | 40.4658 | 1.60584 | ||||||||
\(636\) | 14.9979 | 0.594706 | ||||||||
\(637\) | 1.56056 | 0.0618316 | ||||||||
\(638\) | −9.58081 | −0.379308 | ||||||||
\(639\) | −2.42922 | −0.0960985 | ||||||||
\(640\) | −23.4562 | −0.927187 | ||||||||
\(641\) | −12.6727 | −0.500542 | −0.250271 | − | 0.968176i | \(-0.580520\pi\) | ||||
−0.250271 | + | 0.968176i | \(0.580520\pi\) | |||||||
\(642\) | −25.2049 | −0.994760 | ||||||||
\(643\) | 19.4811 | 0.768260 | 0.384130 | − | 0.923279i | \(-0.374501\pi\) | ||||
0.384130 | + | 0.923279i | \(0.374501\pi\) | |||||||
\(644\) | −18.0663 | −0.711910 | ||||||||
\(645\) | 55.6884 | 2.19273 | ||||||||
\(646\) | 4.21335 | 0.165772 | ||||||||
\(647\) | −37.4744 | −1.47327 | −0.736636 | − | 0.676289i | \(-0.763587\pi\) | ||||
−0.736636 | + | 0.676289i | \(0.763587\pi\) | |||||||
\(648\) | −32.1190 | −1.26175 | ||||||||
\(649\) | −10.5773 | −0.415196 | ||||||||
\(650\) | 38.5896 | 1.51361 | ||||||||
\(651\) | −8.77681 | −0.343990 | ||||||||
\(652\) | 6.47779 | 0.253690 | ||||||||
\(653\) | 16.3762 | 0.640849 | 0.320425 | − | 0.947274i | \(-0.396174\pi\) | ||||
0.320425 | + | 0.947274i | \(0.396174\pi\) | |||||||
\(654\) | 22.5741 | 0.882718 | ||||||||
\(655\) | 39.5675 | 1.54603 | ||||||||
\(656\) | −0.521562 | −0.0203636 | ||||||||
\(657\) | −7.48893 | −0.292171 | ||||||||
\(658\) | 13.8355 | 0.539366 | ||||||||
\(659\) | 19.8667 | 0.773897 | 0.386948 | − | 0.922101i | \(-0.373529\pi\) | ||||
0.386948 | + | 0.922101i | \(0.373529\pi\) | |||||||
\(660\) | 10.5637 | 0.411191 | ||||||||
\(661\) | −27.5440 | −1.07134 | −0.535669 | − | 0.844428i | \(-0.679941\pi\) | ||||
−0.535669 | + | 0.844428i | \(0.679941\pi\) | |||||||
\(662\) | −3.98887 | −0.155032 | ||||||||
\(663\) | −51.8087 | −2.01208 | ||||||||
\(664\) | 42.2720 | 1.64047 | ||||||||
\(665\) | 9.41281 | 0.365013 | ||||||||
\(666\) | −2.53689 | −0.0983027 | ||||||||
\(667\) | 53.8038 | 2.08329 | ||||||||
\(668\) | −19.7620 | −0.764617 | ||||||||
\(669\) | −30.9998 | −1.19852 | ||||||||
\(670\) | 12.0104 | 0.464002 | ||||||||
\(671\) | 6.93773 | 0.267828 | ||||||||
\(672\) | −30.2061 | −1.16522 | ||||||||
\(673\) | 37.5288 | 1.44663 | 0.723315 | − | 0.690518i | \(-0.242617\pi\) | ||||
0.723315 | + | 0.690518i | \(0.242617\pi\) | |||||||
\(674\) | 26.3799 | 1.01612 | ||||||||
\(675\) | 28.1271 | 1.08261 | ||||||||
\(676\) | −17.6172 | −0.677585 | ||||||||
\(677\) | −3.47250 | −0.133459 | −0.0667296 | − | 0.997771i | \(-0.521256\pi\) | ||||
−0.0667296 | + | 0.997771i | \(0.521256\pi\) | |||||||
\(678\) | −15.4498 | −0.593346 | ||||||||
\(679\) | −26.4268 | −1.01417 | ||||||||
\(680\) | 49.0560 | 1.88121 | ||||||||
\(681\) | 47.9484 | 1.83738 | ||||||||
\(682\) | −1.67741 | −0.0642312 | ||||||||
\(683\) | 1.73573 | 0.0664160 | 0.0332080 | − | 0.999448i | \(-0.489428\pi\) | ||||
0.0332080 | + | 0.999448i | \(0.489428\pi\) | |||||||
\(684\) | −1.63656 | −0.0625753 | ||||||||
\(685\) | 4.44970 | 0.170014 | ||||||||
\(686\) | −16.8710 | −0.644139 | ||||||||
\(687\) | 42.4020 | 1.61774 | ||||||||
\(688\) | −1.09330 | −0.0416816 | ||||||||
\(689\) | −31.4059 | −1.19647 | ||||||||
\(690\) | 39.3445 | 1.49782 | ||||||||
\(691\) | 44.5147 | 1.69342 | 0.846709 | − | 0.532056i | \(-0.178580\pi\) | ||||
0.846709 | + | 0.532056i | \(0.178580\pi\) | |||||||
\(692\) | −21.8199 | −0.829468 | ||||||||
\(693\) | 4.07717 | 0.154879 | ||||||||
\(694\) | 24.5347 | 0.931326 | ||||||||
\(695\) | 48.1336 | 1.82581 | ||||||||
\(696\) | 55.3752 | 2.09899 | ||||||||
\(697\) | −16.5090 | −0.625323 | ||||||||
\(698\) | −10.4027 | −0.393747 | ||||||||
\(699\) | 6.66908 | 0.252248 | ||||||||
\(700\) | 25.5841 | 0.966989 | ||||||||
\(701\) | −18.1133 | −0.684128 | −0.342064 | − | 0.939677i | \(-0.611126\pi\) | ||||
−0.342064 | + | 0.939677i | \(0.611126\pi\) | |||||||
\(702\) | 16.0731 | 0.606639 | ||||||||
\(703\) | 2.08729 | 0.0787236 | ||||||||
\(704\) | −6.11785 | −0.230575 | ||||||||
\(705\) | 45.4313 | 1.71104 | ||||||||
\(706\) | −32.8627 | −1.23681 | ||||||||
\(707\) | 25.0362 | 0.941583 | ||||||||
\(708\) | 22.9552 | 0.862709 | ||||||||
\(709\) | 32.6750 | 1.22714 | 0.613568 | − | 0.789642i | \(-0.289734\pi\) | ||||
0.613568 | + | 0.789642i | \(0.289734\pi\) | |||||||
\(710\) | −5.79512 | −0.217487 | ||||||||
\(711\) | 6.02299 | 0.225880 | ||||||||
\(712\) | 4.29087 | 0.160807 | ||||||||
\(713\) | 9.41996 | 0.352780 | ||||||||
\(714\) | 22.7804 | 0.852535 | ||||||||
\(715\) | −22.1206 | −0.827262 | ||||||||
\(716\) | 7.60833 | 0.284336 | ||||||||
\(717\) | −21.0614 | −0.786553 | ||||||||
\(718\) | 23.1416 | 0.863635 | ||||||||
\(719\) | −42.2722 | −1.57649 | −0.788243 | − | 0.615364i | \(-0.789009\pi\) | ||||
−0.788243 | + | 0.615364i | \(0.789009\pi\) | |||||||
\(720\) | 0.737517 | 0.0274856 | ||||||||
\(721\) | −38.3567 | −1.42848 | ||||||||
\(722\) | −0.893036 | −0.0332354 | ||||||||
\(723\) | 17.6796 | 0.657512 | ||||||||
\(724\) | 8.95151 | 0.332680 | ||||||||
\(725\) | −76.1931 | −2.82974 | ||||||||
\(726\) | −18.0173 | −0.668685 | ||||||||
\(727\) | 25.3945 | 0.941830 | 0.470915 | − | 0.882178i | \(-0.343924\pi\) | ||||
0.470915 | + | 0.882178i | \(0.343924\pi\) | |||||||
\(728\) | 38.9360 | 1.44306 | ||||||||
\(729\) | 6.15853 | 0.228094 | ||||||||
\(730\) | −17.8655 | −0.661232 | ||||||||
\(731\) | −34.6062 | −1.27996 | ||||||||
\(732\) | −15.0565 | −0.556504 | ||||||||
\(733\) | −41.9551 | −1.54965 | −0.774823 | − | 0.632179i | \(-0.782161\pi\) | ||||
−0.774823 | + | 0.632179i | \(0.782161\pi\) | |||||||
\(734\) | −23.0543 | −0.850949 | ||||||||
\(735\) | −2.25318 | −0.0831099 | ||||||||
\(736\) | 32.4195 | 1.19500 | ||||||||
\(737\) | −4.28033 | −0.157668 | ||||||||
\(738\) | −4.25287 | −0.156550 | ||||||||
\(739\) | 6.15000 | 0.226232 | 0.113116 | − | 0.993582i | \(-0.463917\pi\) | ||||
0.113116 | + | 0.993582i | \(0.463917\pi\) | |||||||
\(740\) | 9.12515 | 0.335447 | ||||||||
\(741\) | 10.9811 | 0.403400 | ||||||||
\(742\) | 13.8092 | 0.506953 | ||||||||
\(743\) | −23.6412 | −0.867310 | −0.433655 | − | 0.901079i | \(-0.642776\pi\) | ||||
−0.433655 | + | 0.901079i | \(0.642776\pi\) | |||||||
\(744\) | 9.69508 | 0.355439 | ||||||||
\(745\) | 10.0575 | 0.368477 | ||||||||
\(746\) | 8.62391 | 0.315744 | ||||||||
\(747\) | 20.1163 | 0.736015 | ||||||||
\(748\) | −6.56454 | −0.240024 | ||||||||
\(749\) | 34.9918 | 1.27857 | ||||||||
\(750\) | −21.8162 | −0.796615 | ||||||||
\(751\) | −35.8648 | −1.30872 | −0.654362 | − | 0.756182i | \(-0.727063\pi\) | ||||
−0.654362 | + | 0.756182i | \(0.727063\pi\) | |||||||
\(752\) | −0.891926 | −0.0325252 | ||||||||
\(753\) | −16.8900 | −0.615505 | ||||||||
\(754\) | −43.5400 | −1.58563 | ||||||||
\(755\) | 1.09089 | 0.0397015 | ||||||||
\(756\) | 10.6561 | 0.387559 | ||||||||
\(757\) | 21.8139 | 0.792839 | 0.396419 | − | 0.918070i | \(-0.370253\pi\) | ||||
0.396419 | + | 0.918070i | \(0.370253\pi\) | |||||||
\(758\) | −21.9515 | −0.797315 | ||||||||
\(759\) | −14.0218 | −0.508959 | ||||||||
\(760\) | −10.3976 | −0.377161 | ||||||||
\(761\) | −24.2093 | −0.877586 | −0.438793 | − | 0.898588i | \(-0.644594\pi\) | ||||
−0.438793 | + | 0.898588i | \(0.644594\pi\) | |||||||
\(762\) | −20.7574 | −0.751960 | ||||||||
\(763\) | −31.3395 | −1.13457 | ||||||||
\(764\) | 29.2644 | 1.05875 | ||||||||
\(765\) | 23.3446 | 0.844026 | ||||||||
\(766\) | 16.1589 | 0.583846 | ||||||||
\(767\) | −48.0686 | −1.73566 | ||||||||
\(768\) | 34.1149 | 1.23102 | ||||||||
\(769\) | −35.2891 | −1.27256 | −0.636279 | − | 0.771459i | \(-0.719527\pi\) | ||||
−0.636279 | + | 0.771459i | \(0.719527\pi\) | |||||||
\(770\) | 9.72645 | 0.350517 | ||||||||
\(771\) | 39.4742 | 1.42163 | ||||||||
\(772\) | −29.4593 | −1.06026 | ||||||||
\(773\) | 9.97739 | 0.358862 | 0.179431 | − | 0.983771i | \(-0.442574\pi\) | ||||
0.179431 | + | 0.983771i | \(0.442574\pi\) | |||||||
\(774\) | −8.91487 | −0.320439 | ||||||||
\(775\) | −13.3399 | −0.479182 | ||||||||
\(776\) | 29.1917 | 1.04792 | ||||||||
\(777\) | 11.2854 | 0.404861 | ||||||||
\(778\) | 4.19175 | 0.150281 | ||||||||
\(779\) | 3.49915 | 0.125370 | ||||||||
\(780\) | 48.0067 | 1.71892 | ||||||||
\(781\) | 2.06529 | 0.0739020 | ||||||||
\(782\) | −24.4497 | −0.874320 | ||||||||
\(783\) | −31.7354 | −1.13413 | ||||||||
\(784\) | 0.0442355 | 0.00157984 | ||||||||
\(785\) | −56.4733 | −2.01562 | ||||||||
\(786\) | −20.2965 | −0.723953 | ||||||||
\(787\) | −49.6948 | −1.77143 | −0.885714 | − | 0.464232i | \(-0.846330\pi\) | ||||
−0.885714 | + | 0.464232i | \(0.846330\pi\) | |||||||
\(788\) | −3.93511 | −0.140183 | ||||||||
\(789\) | −0.832823 | −0.0296493 | ||||||||
\(790\) | 14.3684 | 0.511204 | ||||||||
\(791\) | 21.4488 | 0.762633 | ||||||||
\(792\) | −4.50374 | −0.160033 | ||||||||
\(793\) | 31.5286 | 1.11961 | ||||||||
\(794\) | −7.61361 | −0.270197 | ||||||||
\(795\) | 45.3449 | 1.60822 | ||||||||
\(796\) | 24.9271 | 0.883518 | ||||||||
\(797\) | 38.0061 | 1.34625 | 0.673123 | − | 0.739531i | \(-0.264952\pi\) | ||||
0.673123 | + | 0.739531i | \(0.264952\pi\) | |||||||
\(798\) | −4.82840 | −0.170923 | ||||||||
\(799\) | −28.2321 | −0.998781 | ||||||||
\(800\) | −45.9101 | −1.62317 | ||||||||
\(801\) | 2.04193 | 0.0721479 | ||||||||
\(802\) | −13.5291 | −0.477729 | ||||||||
\(803\) | 6.36700 | 0.224686 | ||||||||
\(804\) | 9.28930 | 0.327608 | ||||||||
\(805\) | −54.6217 | −1.92516 | ||||||||
\(806\) | −7.62298 | −0.268508 | ||||||||
\(807\) | −22.1688 | −0.780380 | ||||||||
\(808\) | −27.6556 | −0.972920 | ||||||||
\(809\) | 2.22009 | 0.0780543 | 0.0390272 | − | 0.999238i | \(-0.487574\pi\) | ||||
0.0390272 | + | 0.999238i | \(0.487574\pi\) | |||||||
\(810\) | −36.4630 | −1.28118 | ||||||||
\(811\) | 30.1952 | 1.06030 | 0.530149 | − | 0.847904i | \(-0.322136\pi\) | ||||
0.530149 | + | 0.847904i | \(0.322136\pi\) | |||||||
\(812\) | −28.8662 | −1.01300 | ||||||||
\(813\) | −28.7305 | −1.00762 | ||||||||
\(814\) | 2.15684 | 0.0755971 | ||||||||
\(815\) | 19.5850 | 0.686033 | ||||||||
\(816\) | −1.46857 | −0.0514101 | ||||||||
\(817\) | 7.33492 | 0.256616 | ||||||||
\(818\) | −31.2486 | −1.09258 | ||||||||
\(819\) | 18.5287 | 0.647446 | ||||||||
\(820\) | 15.2975 | 0.534211 | ||||||||
\(821\) | 17.2989 | 0.603737 | 0.301868 | − | 0.953350i | \(-0.402390\pi\) | ||||
0.301868 | + | 0.953350i | \(0.402390\pi\) | |||||||
\(822\) | −2.28252 | −0.0796120 | ||||||||
\(823\) | 8.08683 | 0.281889 | 0.140945 | − | 0.990017i | \(-0.454986\pi\) | ||||
0.140945 | + | 0.990017i | \(0.454986\pi\) | |||||||
\(824\) | 42.3697 | 1.47602 | ||||||||
\(825\) | 19.8567 | 0.691320 | ||||||||
\(826\) | 21.1359 | 0.735411 | ||||||||
\(827\) | −12.2290 | −0.425244 | −0.212622 | − | 0.977135i | \(-0.568200\pi\) | ||||
−0.212622 | + | 0.977135i | \(0.568200\pi\) | |||||||
\(828\) | 9.49680 | 0.330036 | ||||||||
\(829\) | 53.1727 | 1.84676 | 0.923382 | − | 0.383883i | \(-0.125413\pi\) | ||||
0.923382 | + | 0.383883i | \(0.125413\pi\) | |||||||
\(830\) | 47.9891 | 1.66573 | ||||||||
\(831\) | 30.4194 | 1.05524 | ||||||||
\(832\) | −27.8026 | −0.963882 | ||||||||
\(833\) | 1.40019 | 0.0485136 | ||||||||
\(834\) | −24.6906 | −0.854967 | ||||||||
\(835\) | −59.7488 | −2.06769 | ||||||||
\(836\) | 1.39138 | 0.0481219 | ||||||||
\(837\) | −5.55623 | −0.192051 | ||||||||
\(838\) | −15.4291 | −0.532989 | ||||||||
\(839\) | 17.6150 | 0.608137 | 0.304068 | − | 0.952650i | \(-0.401655\pi\) | ||||
0.304068 | + | 0.952650i | \(0.401655\pi\) | |||||||
\(840\) | −56.2170 | −1.93967 | ||||||||
\(841\) | 56.9675 | 1.96440 | ||||||||
\(842\) | −8.59984 | −0.296370 | ||||||||
\(843\) | −38.7710 | −1.33534 | ||||||||
\(844\) | −1.20249 | −0.0413913 | ||||||||
\(845\) | −53.2641 | −1.83234 | ||||||||
\(846\) | −7.27286 | −0.250046 | ||||||||
\(847\) | 25.0133 | 0.859467 | ||||||||
\(848\) | −0.890231 | −0.0305707 | ||||||||
\(849\) | −6.91641 | −0.237370 | ||||||||
\(850\) | 34.6239 | 1.18759 | ||||||||
\(851\) | −12.1124 | −0.415206 | ||||||||
\(852\) | −4.48217 | −0.153557 | ||||||||
\(853\) | 15.7499 | 0.539265 | 0.269632 | − | 0.962963i | \(-0.413098\pi\) | ||||
0.269632 | + | 0.962963i | \(0.413098\pi\) | |||||||
\(854\) | −13.8632 | −0.474388 | ||||||||
\(855\) | −4.94798 | −0.169217 | ||||||||
\(856\) | −38.6528 | −1.32113 | ||||||||
\(857\) | −20.1489 | −0.688272 | −0.344136 | − | 0.938920i | \(-0.611828\pi\) | ||||
−0.344136 | + | 0.938920i | \(0.611828\pi\) | |||||||
\(858\) | 11.3470 | 0.387379 | ||||||||
\(859\) | 25.0443 | 0.854501 | 0.427250 | − | 0.904133i | \(-0.359482\pi\) | ||||
0.427250 | + | 0.904133i | \(0.359482\pi\) | |||||||
\(860\) | 32.0666 | 1.09346 | ||||||||
\(861\) | 18.9189 | 0.644755 | ||||||||
\(862\) | 22.5609 | 0.768429 | ||||||||
\(863\) | −3.99470 | −0.135981 | −0.0679906 | − | 0.997686i | \(-0.521659\pi\) | ||||
−0.0679906 | + | 0.997686i | \(0.521659\pi\) | |||||||
\(864\) | −19.1222 | −0.650549 | ||||||||
\(865\) | −65.9705 | −2.24306 | ||||||||
\(866\) | −11.2565 | −0.382513 | ||||||||
\(867\) | −10.9835 | −0.373021 | ||||||||
\(868\) | −5.05388 | −0.171540 | ||||||||
\(869\) | −5.12068 | −0.173707 | ||||||||
\(870\) | 62.8645 | 2.13131 | ||||||||
\(871\) | −19.4520 | −0.659105 | ||||||||
\(872\) | 34.6183 | 1.17232 | ||||||||
\(873\) | 13.8916 | 0.470161 | ||||||||
\(874\) | 5.18221 | 0.175291 | ||||||||
\(875\) | 30.2873 | 1.02390 | ||||||||
\(876\) | −13.8179 | −0.466862 | ||||||||
\(877\) | 7.25772 | 0.245076 | 0.122538 | − | 0.992464i | \(-0.460897\pi\) | ||||
0.122538 | + | 0.992464i | \(0.460897\pi\) | |||||||
\(878\) | 0.415578 | 0.0140251 | ||||||||
\(879\) | −11.3600 | −0.383163 | ||||||||
\(880\) | −0.627028 | −0.0211371 | ||||||||
\(881\) | 34.7122 | 1.16948 | 0.584742 | − | 0.811219i | \(-0.301196\pi\) | ||||
0.584742 | + | 0.811219i | \(0.301196\pi\) | |||||||
\(882\) | 0.360701 | 0.0121454 | ||||||||
\(883\) | 34.6895 | 1.16740 | 0.583698 | − | 0.811971i | \(-0.301605\pi\) | ||||
0.583698 | + | 0.811971i | \(0.301605\pi\) | |||||||
\(884\) | −29.8326 | −1.00338 | ||||||||
\(885\) | 69.4030 | 2.33296 | ||||||||
\(886\) | −25.8938 | −0.869919 | ||||||||
\(887\) | 19.9176 | 0.668769 | 0.334384 | − | 0.942437i | \(-0.391472\pi\) | ||||
0.334384 | + | 0.942437i | \(0.391472\pi\) | |||||||
\(888\) | −12.4661 | −0.418335 | ||||||||
\(889\) | 28.8173 | 0.966500 | ||||||||
\(890\) | 4.87120 | 0.163283 | ||||||||
\(891\) | 12.9949 | 0.435344 | ||||||||
\(892\) | −17.8504 | −0.597674 | ||||||||
\(893\) | 5.98392 | 0.200244 | ||||||||
\(894\) | −5.15907 | −0.172545 | ||||||||
\(895\) | 23.0031 | 0.768909 | ||||||||
\(896\) | −16.7040 | −0.558043 | ||||||||
\(897\) | −63.7222 | −2.12762 | ||||||||
\(898\) | 26.6626 | 0.889741 | ||||||||
\(899\) | 15.0512 | 0.501985 | ||||||||
\(900\) | −13.4487 | −0.448289 | ||||||||
\(901\) | −28.1785 | −0.938761 | ||||||||
\(902\) | 3.61574 | 0.120391 | ||||||||
\(903\) | 39.6578 | 1.31973 | ||||||||
\(904\) | −23.6929 | −0.788014 | ||||||||
\(905\) | 27.0641 | 0.899641 | ||||||||
\(906\) | −0.559582 | −0.0185909 | ||||||||
\(907\) | 24.3288 | 0.807825 | 0.403913 | − | 0.914798i | \(-0.367650\pi\) | ||||
0.403913 | + | 0.914798i | \(0.367650\pi\) | |||||||
\(908\) | 27.6097 | 0.916261 | ||||||||
\(909\) | −13.1607 | −0.436511 | ||||||||
\(910\) | 44.2019 | 1.46528 | ||||||||
\(911\) | −33.5883 | −1.11283 | −0.556416 | − | 0.830904i | \(-0.687824\pi\) | ||||
−0.556416 | + | 0.830904i | \(0.687824\pi\) | |||||||
\(912\) | 0.311269 | 0.0103071 | ||||||||
\(913\) | −17.1026 | −0.566014 | ||||||||
\(914\) | −31.7772 | −1.05110 | ||||||||
\(915\) | −45.5220 | −1.50491 | ||||||||
\(916\) | 24.4160 | 0.806727 | ||||||||
\(917\) | 28.1775 | 0.930504 | ||||||||
\(918\) | 14.4213 | 0.475974 | ||||||||
\(919\) | −41.9286 | −1.38310 | −0.691549 | − | 0.722329i | \(-0.743071\pi\) | ||||
−0.691549 | + | 0.722329i | \(0.743071\pi\) | |||||||
\(920\) | 60.3365 | 1.98923 | ||||||||
\(921\) | −48.1120 | −1.58534 | ||||||||
\(922\) | 1.38700 | 0.0456783 | ||||||||
\(923\) | 9.38574 | 0.308936 | ||||||||
\(924\) | 7.52281 | 0.247482 | ||||||||
\(925\) | 17.1526 | 0.563975 | ||||||||
\(926\) | −1.54766 | −0.0508592 | ||||||||
\(927\) | 20.1628 | 0.662232 | ||||||||
\(928\) | 51.7997 | 1.70041 | ||||||||
\(929\) | −38.9179 | −1.27685 | −0.638427 | − | 0.769683i | \(-0.720414\pi\) | ||||
−0.638427 | + | 0.769683i | \(0.720414\pi\) | |||||||
\(930\) | 11.0063 | 0.360911 | ||||||||
\(931\) | −0.296775 | −0.00972641 | ||||||||
\(932\) | 3.84021 | 0.125790 | ||||||||
\(933\) | 14.6153 | 0.478485 | ||||||||
\(934\) | −25.7123 | −0.841332 | ||||||||
\(935\) | −19.8473 | −0.649077 | ||||||||
\(936\) | −20.4673 | −0.668994 | ||||||||
\(937\) | 58.4744 | 1.91027 | 0.955137 | − | 0.296164i | \(-0.0957076\pi\) | ||||
0.955137 | + | 0.296164i | \(0.0957076\pi\) | |||||||
\(938\) | 8.55307 | 0.279268 | ||||||||
\(939\) | 48.5013 | 1.58278 | ||||||||
\(940\) | 26.1603 | 0.853255 | ||||||||
\(941\) | 11.2067 | 0.365328 | 0.182664 | − | 0.983175i | \(-0.441528\pi\) | ||||
0.182664 | + | 0.983175i | \(0.441528\pi\) | |||||||
\(942\) | 28.9686 | 0.943847 | ||||||||
\(943\) | −20.3053 | −0.661230 | ||||||||
\(944\) | −1.36255 | −0.0443472 | ||||||||
\(945\) | 32.2178 | 1.04805 | ||||||||
\(946\) | 7.57932 | 0.246425 | ||||||||
\(947\) | −44.4900 | −1.44573 | −0.722866 | − | 0.690989i | \(-0.757175\pi\) | ||||
−0.722866 | + | 0.690989i | \(0.757175\pi\) | |||||||
\(948\) | 11.1131 | 0.360935 | ||||||||
\(949\) | 28.9349 | 0.939265 | ||||||||
\(950\) | −7.33867 | −0.238098 | ||||||||
\(951\) | −21.3617 | −0.692702 | ||||||||
\(952\) | 34.9347 | 1.13224 | ||||||||
\(953\) | −57.2567 | −1.85473 | −0.927363 | − | 0.374164i | \(-0.877930\pi\) | ||||
−0.927363 | + | 0.374164i | \(0.877930\pi\) | |||||||
\(954\) | −7.25904 | −0.235020 | ||||||||
\(955\) | 88.4784 | 2.86309 | ||||||||
\(956\) | −12.1276 | −0.392235 | ||||||||
\(957\) | −22.4040 | −0.724217 | ||||||||
\(958\) | −6.00261 | −0.193936 | ||||||||
\(959\) | 3.16880 | 0.102326 | ||||||||
\(960\) | 40.1423 | 1.29559 | ||||||||
\(961\) | −28.3648 | −0.914995 | ||||||||
\(962\) | 9.80176 | 0.316021 | ||||||||
\(963\) | −18.3940 | −0.592738 | ||||||||
\(964\) | 10.1803 | 0.327886 | ||||||||
\(965\) | −89.0676 | −2.86719 | ||||||||
\(966\) | 28.0188 | 0.901489 | ||||||||
\(967\) | −11.2747 | −0.362571 | −0.181286 | − | 0.983431i | \(-0.558026\pi\) | ||||
−0.181286 | + | 0.983431i | \(0.558026\pi\) | |||||||
\(968\) | −27.6303 | −0.888071 | ||||||||
\(969\) | 9.85259 | 0.316511 | ||||||||
\(970\) | 33.1398 | 1.06405 | ||||||||
\(971\) | 10.1284 | 0.325035 | 0.162517 | − | 0.986706i | \(-0.448039\pi\) | ||||
0.162517 | + | 0.986706i | \(0.448039\pi\) | |||||||
\(972\) | −15.8544 | −0.508530 | ||||||||
\(973\) | 34.2778 | 1.09890 | ||||||||
\(974\) | 25.0945 | 0.804080 | ||||||||
\(975\) | 90.2388 | 2.88995 | ||||||||
\(976\) | 0.893707 | 0.0286069 | ||||||||
\(977\) | 17.5695 | 0.562097 | 0.281049 | − | 0.959694i | \(-0.409318\pi\) | ||||
0.281049 | + | 0.959694i | \(0.409318\pi\) | |||||||
\(978\) | −10.0463 | −0.321246 | ||||||||
\(979\) | −1.73602 | −0.0554835 | ||||||||
\(980\) | −1.29743 | −0.0414450 | ||||||||
\(981\) | 16.4741 | 0.525976 | ||||||||
\(982\) | −4.99323 | −0.159340 | ||||||||
\(983\) | 19.2044 | 0.612524 | 0.306262 | − | 0.951947i | \(-0.400922\pi\) | ||||
0.306262 | + | 0.951947i | \(0.400922\pi\) | |||||||
\(984\) | −20.8983 | −0.666213 | ||||||||
\(985\) | −11.8975 | −0.379085 | ||||||||
\(986\) | −39.0656 | −1.24410 | ||||||||
\(987\) | 32.3533 | 1.02982 | ||||||||
\(988\) | 6.32314 | 0.201166 | ||||||||
\(989\) | −42.5639 | −1.35345 | ||||||||
\(990\) | −5.11285 | −0.162497 | ||||||||
\(991\) | −9.04212 | −0.287232 | −0.143616 | − | 0.989633i | \(-0.545873\pi\) | ||||
−0.143616 | + | 0.989633i | \(0.545873\pi\) | |||||||
\(992\) | 9.06908 | 0.287944 | ||||||||
\(993\) | −9.32765 | −0.296004 | ||||||||
\(994\) | −4.12693 | −0.130898 | ||||||||
\(995\) | 75.3649 | 2.38923 | ||||||||
\(996\) | 37.1166 | 1.17609 | ||||||||
\(997\) | 44.1747 | 1.39903 | 0.699513 | − | 0.714620i | \(-0.253400\pi\) | ||||
0.699513 | + | 0.714620i | \(0.253400\pi\) | |||||||
\(998\) | −20.9120 | −0.661958 | ||||||||
\(999\) | 7.14429 | 0.226035 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4009.2.a.c.1.31 | ✓ | 71 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4009.2.a.c.1.31 | ✓ | 71 | 1.1 | even | 1 | trivial |